Update
This commit is contained in:
parent
30e9a21065
commit
995a822cae
@ -337,11 +337,14 @@ Qed.
|
|||||||
Various general properties of a subsequence.
|
Various general properties of a subsequence.
|
||||||
*)
|
*)
|
||||||
|
|
||||||
Theorem subsequence2_app {X: Type} :
|
Theorem subsequence_app {X: Type} :
|
||||||
forall l1 s1 l2 s2 : list X,
|
forall l1 s1 l2 s2 : list X,
|
||||||
subsequence2 l1 s1 -> subsequence2 l2 s2 -> subsequence2 (l1++l2) (s1++s2).
|
subsequence l1 s1 -> subsequence l2 s2 -> subsequence (l1++l2) (s1++s2).
|
||||||
Proof.
|
Proof.
|
||||||
intros l1 s1 l2 s2. intros H I.
|
intros l1 s1 l2 s2. intros H I.
|
||||||
|
apply subsequence_eq_def_3. apply subsequence_eq_def_2.
|
||||||
|
apply subsequence_eq_def_1 in H.
|
||||||
|
apply subsequence_eq_def_1 in I.
|
||||||
destruct H. destruct I. exists (x++x0). destruct H. destruct H0.
|
destruct H. destruct I. exists (x++x0). destruct H. destruct H0.
|
||||||
split. rewrite app_length. rewrite app_length.
|
split. rewrite app_length. rewrite app_length.
|
||||||
rewrite H. rewrite H0. reflexivity.
|
rewrite H. rewrite H0. reflexivity.
|
||||||
@ -363,9 +366,11 @@ Qed.
|
|||||||
|
|
||||||
Theorem subsequence_trans {X: Type} :
|
Theorem subsequence_trans {X: Type} :
|
||||||
forall (l1 l2 l3: list X),
|
forall (l1 l2 l3: list X),
|
||||||
subsequence l1 l2 -> subsequence2 l2 l3 -> subsequence2 l1 l3.
|
subsequence l1 l2 -> subsequence l2 l3 -> subsequence l1 l3.
|
||||||
Proof.
|
Proof.
|
||||||
intros l1 l2 l3. intros H I.
|
intros l1 l2 l3. intros H I.
|
||||||
|
apply subsequence_eq_def_3. apply subsequence_eq_def_2.
|
||||||
|
apply subsequence_eq_def_1 in I.
|
||||||
destruct H. destruct H. destruct H. destruct I. destruct H1.
|
destruct H. destruct H. destruct H. destruct I. destruct H1.
|
||||||
exists (
|
exists (
|
||||||
(repeat false (length x)) ++
|
(repeat false (length x)) ++
|
||||||
|
Loading…
Reference in New Issue
Block a user